Answer:
Approximately 34% of people sleep between 6 and 7.5 hours per night
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 6
Standard deviation = 1.5
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
What percentage of people sleep between 6 and 7.5 hours per night
6 is the mean.
7.5 is 1 one standard deviation above the mean.
By the Empirical Rule, of the 50% of the measures that are above the mean, 68% are within 1 standard deviation of the mean(between 6 and 7.5).
0.5*0.68 = 0.34
Approximately 34% of people sleep between 6 and 7.5 hours per night
